Semiconductor memory devices, memory systems including semiconductor memory devices, and operating methods of semiconductor memory devices

A semiconductor memory device includes a memory core that performs reading and writing of data, data delivery and training blocks that are connected between first pads and the memory core, and at least one data delivery, clock generation and training block that is connected between at least one second pad and the memory core. In a first training operation, the data delivery and training blocks output first training data, received through the first pads, through the first pads as second training data. In a second training operation, at least one of the data delivery and training blocks outputs third training data, received through the at least one second pad, through at least one of the first pads as fourth training data. The second training data and the fourth training data are output in synchronization with read data strobe signals output through the at least one second pad.